Explain how the nuclear shell model predicts the existence of magic numbers. Using shell model, predict the spin parity or characteristics of ground state of ^{15}_8\text{O}, ^{16}_8\text{O} and ^{17}_8\text{O}.

A reactor is developing nuclear energy at a rate of 3\cdot 2 \times 10^7\text{ watts}. How many atoms of \text{U}^{235} undergo fission per second? How many kg of \text{U}^{235} would be used up in 1000 hours of operation? Assume that an average energy of 200\text{ MeV} is released per fission. Take Avogadro number as 6 \times 10^{23} and 1\text{ MeV} = 1\cdot 6 \times 10^{-13}\text{ joule}.

(i) The radius of a nucleus is given to be 3\cdot 46\text{ fermi}. Estimate the mass number A of the nucleus and identify the nucleus. (ii) What is Bohr magneton? Find out the ratio of nuclear magnetic moment to Bohr magneton.

(i) Show that pion decay, muon decay and pair production conserve lepton numbers L_e and L_\mu. (ii) Which of the following reactions is/are possible? Justify with reason : \bar{\nu}_e + p = n + \mu^+ \bar{\nu}_e + p \rightarrow n + e^+

(i) What is Q-value and how does it help to study the kinematics of a nuclear reaction? (ii) Prove that ^{252}\text{Cf} can undergo spontaneous fission as under : ^{252}\text{Cf} = {}^{98}\text{Zr} + {}^{145}\text{Ce} + 9 {}^{1}\text{n} Given : \begin{aligned} M(^{252}\text{Cf}) &= 252\cdot 081621\text{ a.m.u.}\\ M(^{98}\text{Zr}) &= 97\cdot 912735\text{ a.m.u.}\\ M(^{145}\text{Ce}) &= 144\cdot 917230\text{ a.m.u.}\\ M(^{1}\text{n}) &= 1\cdot 008665\text{ a.m.u.} \end{aligned}

What do you mean by strength of interaction among the elementary particles? Calculate the dimensionless coupling constants of gravitational and electromagnetic interactions.

Which of the following reactions are possible ? (i) \quad \pi^+ + n^0 \rightarrow \Lambda^0 + K^+ (ii) \quad \pi^+ + n^0 \rightarrow K^0 + K^+ (iii) \quad \pi^+ + n \rightarrow \pi^- + p

(i) Describe the Quark model of hadrons, including the properties of quark. (ii) How does an up quark become a down quark ?

Delhi requires 3000\text{ MWh} of electric energy per day. It is to be supplied by a reactor which converts nuclear energy into electrical energy with an efficiency of 20\text{ percent}. If reactor uses nuclear fuel of \text{U}^{235}, calculate the mass of \text{U}^{235} needed for one day operation.

(i) What is nuclear binding energy and how does it vary with mass number of the nucleus ? (ii) Calculate the binding energy per nucleon of ^{4}\text{He}. Given m (^{4}\text{He}) = 4\cdot 002602\text{ u}, m_p = 1\cdot 007825\text{ u} and m_n = 1\cdot 008665\text{ u}.

Calculate the mass of deuterium nucleus if the binding energy per nucleon is 1\text{ MeV}.

A sample of uranium emitting \alpha-particles of energy 4\cdot 18\text{ MeV} is placed near the ionization chamber. Assuming that only 10 particles per second enter the chamber, calculate the current produced. Given 1 ion pair requires 35\text{ eV}.

Assuming that protons and neutrons possess equal masses, calculate how many times nuclear matter is denser than water if nuclear radius is given by 1\cdot 2 \times 10^{-15} A^{1/3}\text{ m}, where A is the mass number.

(i) Plot mass number A versus binding energy per nucleon. How does this curve help to explain the nuclear fission and fusion ? (ii) In their old age, heavy stars obtain part of their energy by the following nuclear reaction {^{4}_{2}\text{He}} + {^{12}_{6}\text{C}} = {^{16}_{8}\text{O}}. How much energy does each such event give off ? [\text{Given : } {^{4}_{2}\text{He}} = 4\cdot 002603\text{ u}, {^{12}_{6}\text{C}} = 12\cdot 000000\text{ u}, {^{16}_{8}\text{O}} = 15\cdot 999\text{ u}]

(i) Write semi-empirical mass formula for the nuclei. Discuss in brief the physical significance of each term. (ii) The meson theory of nuclear forces assumes the virtual exchange of pions. If a nucleon emits a virtual pion of rest mass 270\text{ m}_{\text{e}}, calculate the range of the nuclear force. (\text{m}_{\text{e}} is the mass of electron = 9\cdot 11 \times 10^{-31}\text{ kg})

(i) Plot proton number (Z) versus neutron number (N). What is the inference from the plot with regards to light and heavy nuclides ? (ii) Which nucleus would you expect to be more stable, ^{7}_{3}\text{Li} or ^{8}_{3}\text{Li} ? Justify your answer.

Discuss in brief any two basic nuclear properties. Find the nuclear radius of ^{12}_{6}\text{C} nucleus. Compare the atomic radius of carbon C-12 to the nuclear radius assuming the atomic radius to be 0\cdot 529 \times 10^{-10}\text{ m}. (R_0 = 1\cdot 2\text{ fm}) What inference will you get from the comparison with regards to nuclear size of carbon ?

A nuclear reactor using ^{235}_{92}\text{U} is to operate at a power level of 250 megawatt. If the energy released per fission of ^{235}_{92}\text{U} is 200\text{ MeV}, calculate the rate of consumption per year.

Show that pion decay, muon decay and pair production conserve the Lepton numbers \text{L}_{\text{e}} and \text{L}_{\mu}.